Gao, G. and Sun, Z. (2016) Two alternating Direction Implicit Difference Schems for Two-Dimensional Distributed-Order Fractional Diffusion Equations. Journal of Scientific Computing, 69, 506-531.
https://doi.org/10.1007/s10915-016-0208-7

has been cited by the following article:

• TITLE: ADI Finite Element Method for 2D Nonlinear Time Fractional Reaction-Subdiffusion Equation

  AUTHORS: Peng Zhu, Shenglan Xie

  KEYWORDS: Nonlinear Fractional Differential Equation, Alternating Direction Implicit Method, Finite Element Method, Riemann-Liouville Fractional Derivative

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.6 No.4, December 21, 2016

  ABSTRACT: In this paper, an alternating direction Galerkin finite element method is presented for solving 2D time fractional reaction sub-diffusion equation with nonlinear source term. Firstly, one order implicit-explicit method is used for time discretization, then Galerkin finite element method is adopted for spatial discretization and obtain a fully discrete linear system. Secondly, Galerkin alternating direction procedure for the system is derived by adding an extra term. Finally, the stability and convergence of the method are analyzed rigorously. Numerical results confirm the accuracy and efficiency of the proposed method.